To run WordPress with Inkwell you need a web host, that has the minimum requirements:
PHP version 5.3 and later
MySQL version 5.0 and later
The mod_rewrite Apache module
There are many hosts that will be suitable for these parameters. You can contact with your potential host and ask them, are the hosting compatible with WordPress. Or you can find companies that specialize in WordPress-sites hosting, for example Bluehost. Please note that while we receive a small commission if you choose bluehost, our recommendation is based on the quality of their products and is not based on compensation.